ON RESAMPLING SCHEMES FOR PARTICLE FILTERS WITH WEAKLY INFORMATIVE OBSERVATIONS

• 成果类型: Article
• 署名作者: Chopin, Nicolas; Singh, Sumeetpal S.; Soto, Tomas; Vihola, Matti
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; University of Cambridge; Lappeenranta-Lahti University of Technology LUT; University of Jyvaskyla
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2222
• 发表日期: 2022
• 页码: 3197-3222

摘要

We consider particle filters with weakly informative observations (or 'po-tentials') relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous -time Feynman-Kac path integral models-a scenario that naturally arises when addressing filtering and smoothing problems in continuous time-but our findings are indicative about weakly informative settings beyond this con-text too. We study the performance of different resampling schemes, such as systematic resampling, SSP (Srinivasan sampling process) and stratified resampling, as the time-discretisation becomes finer and also identify their continuous-time limit, which is expressed as a suitably defined 'infinitesimal generator.' By contrasting these generators, we find that (certain modifica-tions of) systematic and SSP resampling 'dominate' stratified and indepen-dent 'killing' resampling in terms of their limiting overall resampling rate. The reduced intensity of resampling manifests itself in lower variance in our numerical experiment. This efficiency result, through an ordering of the re -sampling rate, is new to the literature. The second major contribution of this work concerns the analysis of the limiting behaviour of the entire population of particles of the particle filter as the time discretisation becomes finer. We provide the first proof, under general conditions, that the particle approxima-tion of the discretised continuous-time Feynman-Kac path integral models converges to a (uniformly weighted) continuous-time particle system.